Anti-reflective coatings on optical waveguides

ABSTRACT

An anti-reflective waveguide assembly comprising a waveguide substrate having a first index of refraction, a plurality of diffractive optical elements disposed upon a first surface of the waveguide and an anti-reflective coating disposed upon a second surface of the waveguide. The anti-reflective coating preferably increases absorption of light through a surface to which it is applied into the waveguide so that at least 97 percent of the light is transmitted. The anti-reflective coating is composed of four layers of material having different indices of refraction that the first index of refraction and an imaginary refractive index less than 1×10 −3  but preferably less than 5×10 −4 .

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication No. 62/596,904, filed on Dec. 10, 2017 and, U.S. ProvisionalPatent Application No. 62/751,240, filed on Oct. 26, 2018, each of whichis incorporated herein by reference in their entirety

BACKGROUND OF THE INVENTION

Surface treatments of substrates such as windows or photovoltaic devices(e.g. solar energy panels) benefit from a coating of layeredanti-reflective material. Reduction of glare from light impacting glass,improved retention of natural light for energy costs, or increasedabsorption of light impacting a photovoltaic cell are some of the waysanti-reflective coatings are used. Conventional anti-reflective coatingsprovide benefits for substantially orthogonal light paths, relative tonormal of a surface of a substrate, but are generally directed tomaximize anti-reflection for such freespace light that anticipatesorigination of light completely external to a substrate. Conventionalcoatings also seek to increase transmission rates. Certain opticalmediums manipulate light paths other than freespace origination, andantireflection coatings to optimize the performance of such mediums areneeded.

SUMMARY

Embodiments of the present invention are generally directed to specificmaterials and thicknesses of layers for anti-reflective coatings inoptical waveguides. More specifically, the embodiments and techniquesdescribed herein relate to anti-reflective coatings that must facilitatelight propagation for total internal reflection (TIR), andsimultaneously minimize light reflection at orthogonal angles or otherfreespace light. Embodiments described herein are directed away fromseeking complete transmission of light.

Some embodiments are directed to a waveguide substrate having a firstindex of refraction, such as glass. The substrate may be planar, orcylindrical (such as a fiber optic). For planar substrates, a pluralityof diffractive optical elements, such as a grating, is disposed upon afirst surface, and an anti-reflective coating is disposed upon theopposite surface. For cylindrical waveguides, an anti-reflective coatingis applied to the outer surface.

In some embodiments, the waveguide is configured to receive light, andpropagate it along an axis by total internal reflection. In planarwaveguides, the light travels in along such an axis in a firstdirection, and outcouples light in a substantially orthogonal directionwhen the light reflects off of a diffractive optical element of thatcorresponding surface. In cylindrical waveguides, the light reflectsalong the waveguide along an axis substantially parallel to the lengthof the waveguides, and outcouples at a distal end.

The anti-reflective coating on such embodiments is configured tominimize the phase retardation as between the s and p polarizationstates of the received light, such that the angle of bounce by TIR foreach polarization component of light is substantially similar.

In some embodiments, the anti-reflective coating is a single layer ofmagnesium fluoride (MgF₂) having a thickness between 75 and 125nanometers (nm). In some embodiments, a layer of silica (SiO₂) isapplied as an outer layer to the coating.

In some embodiments, the anti-reflective coating has an imaginaryrefractive index value (alternatively referred to herein as anabsorption coefficient), k, less than 5×10⁻⁴. In some embodiments the kvalue of the complete coating is between 5×10⁻⁴ and 1×10⁻³, regardlessof the number of layers comprising the coating. In some embodiments, thecoating is a single layer of material. In some embodiments, the coatingalternates between two materials, with one material having acomparatively higher index of refraction than the second material. Insome embodiments, less than eight total layers are utilized.

In some embodiments, titania (TiO₂) with an index of refraction greaterthan 2 is utilized as a coating layer material; in some embodiments,SiO₂ with an index of refraction between 1.45 and 1.58 alternates layerswith titania.

These materials and layer selections optimize the efficiency of lightoutput by an optical waveguide, minimize phase retardation to reduceoptical defects such as striations in images output by such a waveguide,and minimize the labor and material cost of conventional layers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top-down view showing an anti-reflective coating asunderstood with respect to its function to minimize reflected light andmaximize absorption of light into a waveguide.

FIG. 2 is a top-down view showing a planar waveguide outcoupling aplurality of beams that propagate through the waveguide by totalinternal reflection according to some embodiments.

FIG. 3 is a top-down view showing a multi-waveguide stack outcoupling aplurality of beams as light bundles according to some embodiments.

FIG. 4 is a front view of a planar waveguide having three diffractiveoptical element regions according to some embodiments.

FIG. 5 is a front view showing an orthogonal pupil expander diffractinglight across its span according to some embodiments.

FIG. 6A is a top-down view showing a plurality of light bounces througha waveguide according to some embodiments.

FIG. 6B is a front view of an inferometer network of energy transmittedthrough a waveguide configured to support total internal reflectionaccording to some embodiments.

FIG. 7 is a graph illustrating a phase retardation relationship as afunction of layers in an anti-reflective coating according to someembodiments.

FIG. 8A shows captured images of an eyepiece design for blue (455 nm)light on substrates with different n values of layers of ananti-reflective coating.

FIG. 8B shows simulated images of an eyepiece design for blue (455 nm)light on substrates with different n values of layers of ananti-reflective coating.

FIG. 8C shows captured images an eyepiece design for red (625 nm) lighton substrates with different n values of layers of an anti-reflectivecoating.

FIG. 8D shows simulated images an eyepiece design for red (625 nm) lighton substrates with different n values of layers of an anti-reflectivecoating.

FIGS. 9A-9D are graphs that illustrate efficiency decay of light energyoutput by a waveguide as a function of the number of layers and k valueof an anti-reflective coating according to some embodiments.

DETAILED DESCRIPTION

Antireflection coatings are generally configured to create out-of-phasereflections across layers of material with differing indices ofrefraction. Conventionally, single-layer anti-reflective coatings seek arefractive index, n, equal to the square root of the coated substrate'sindex of refraction, and with a thickness, t, equal to one quarter thewavelength, λ, of the light targeted by the anti-reflective coating.

n _(coating)=√(n _(substrate))  Eq. 1

t=λ _(target light)/(4·n _(coating))  Eq. 2

FIG. 1 depicts anti-reflection, with light L 100 impacting medium 110and reflecting light R 101 while simultaneously transmitting to medium120 and reflecting light R 103 that creates constructive interferencewith light R 101; remaining light L 105 transmits into medium 103. Manyvariations to improve the total amount of transmitted light L 105 areknown. For example, broad band anti-reflection to improve transmissionof multiple wavelengths with a single coating is achieved withadditional and/or varying thickness layers.

Though the coating arrangement show in FIG. 1 may work as intended forfreespace light, some optical systems employ waveguide technology;augmented or mixed reality system in particular maximize this technologyin exit pupil expander systems to deliver light from a source andpropagate that light through waveguides by TIR and then outcoupletowards a user's eye.

FIG. 2 shows a simplified version of such a system. One waveguide isillustrated, but it will be appreciated that other waveguides stackedtogether (as further described below with reference to FIG. 3) mayfunction similarly. Light 400 is injected into the waveguide 1182 at aninput surface 1382 of the waveguide 1182 and propagates within thewaveguide 1182 by TIR. The input surface 1382 may be an incouplinggrating formed by diffractive optical elements to diffract light 400into the waveguide 1382 at angles supporting TIR. At points where thelight 400 impinges upon outcoupling diffractive optical elements 1282,sampled portions exit the waveguide as a plurality of exit beams 402.

Each exit beam is a sampled beamlet of light 400 and increases thelikelihood that any one sampled beamlet will be viewed by an eye 4 of aviewer. It is critical therefore that the waveguide 1182 maintains TIRto create the plurality of exit beams across its span, otherwise theexit beams 402 would not be distributed, and the resulting exit pupil(s)would only be viewable in certain positions of eye 4, limiting theapplicability and flexibility of the system.

FIG. 2 depicts a single waveguide system, but one of skill in the artwill appreciate that if single waveguide 1182 imparts sampled portionsof light 400, additional waveguides performing similar functions mayimpart additional sampled portions to create rich light effects such asmulti-color component images or depth perception. FIG. 3 illustratessuch a multi-layered system with three waveguides 1210, 1220, and 1230propagating light by TIR. As each light path 1240, 1242 and 1244respectively incouples at locations 1212, 1222, and 1232 impact arespective outcoupling diffractive optical element 1214, 1224, or 1234(outcoupled light from paths 1222 and 1232 not depicted) disposed uponwaveguide 1210, 1220, and 1230, it diffracts a plurality of beamlets intwo directions: one towards the viewer (as in eye 4 of FIG. 2)represented by light bundle 3010, and one in a direction away from theviewer represented by light bundle 3020.

The light bundle 3020 may cause undesirable effects if it reflects offof the subsequent waveguide 1220, such as interference with light bundle3010, increased blurriness due to any change in angle that may resultfrom the reflection, etc. Here, an anti-reflective coating applied tothe opposite surface of a waveguide from its outcoupling diffractiveoptical element will be beneficial to reduce these effects. Aconventional coating that attempts to increase transmission generallywill, however, degrade the light paths 1240, 1242, and 1244 as theyprogress across waveguides 1210, 1220, and 1230 by TIR. This degradationintroduces uniformity complications at outcoupling, and results in poorimage quality.

Waveguide optical systems that employ pupil expander technologyaggravate this problem. In a pupil expander system, such as depicted inFIG. 2, not only is light distributed in the substantially verticaldirection, but also in an orthogonal direction to the exit beam path.FIG. 4 depicts an orthogonal pupil expander (OPE) 3706 disposed upon awaveguide 3704. FIG. 4 also depicts an exit pupil expander (EPE) 3708for outcoupling progressive exit beams of TIR light, similar tooutcoupling diffractive optical elements 1282 depicted in FIG. 2, and anincoupling grating (ICG) 3702 similar to the input surface 1382 of FIG.2. In the waveguide system of FIG. 4, light incouples to the waveguidethrough the incoupling grating and diffracts towards the orthogonalpupil expander.

FIG. 5 depicts light sampling across the orthogonal pupil expander.Light 4410B from the incoupling grating of FIG. 4 encounters a grating4420B, such as a series of diffractive optical elements, that diffractssamples of light in a first direction and a sample 4430B of that samelight in a second direction; the particular directions diffracted are afunction of the particular geometries of the diffractive opticalelement.

FIG. 6A depicts a cross-sectional view of this light path, one awaveguide comprising a grating 662 on one surface, and ananti-reflective coating 664 on the opposite surface. As light propagatesby TIR through the waveguide, it alternatively reflects against theorthogonal pupil expander, and a surface opposite the orthogonal pupilexpander. One of skill in the art will appreciate that a similarfunctionality occurs with the exit pupil expander region of thewaveguide. To reduce the reflections described by light bundle 3020 inreference to FIG. 3, an anti-reflective coating is applied to thisopposite surface. A cumulative light inferometer may be derived fromthis interaction, such as the unit cell inferometer depicted by FIG. 6B.In FIG. 6B, each interaction with the orthogonal pupil expander willsample the light into two paths, with a reflection against theanti-reflective coating side between each successive reflection againstthe orthogonal pupil expander. Each reflection off of the orthogonalpupil expander side or the anti-reflection side may further introducepolarization changes to the light, such that each successive bounceperturbs the polarization state and changes the energy at each outputnode.

By breaking down the polarization into the constituent s and p states,the resulting electric field, E, is a function of amplitude, A, andphase, ϕ, of the light, and is depicted for each s and p path asfollows:

E _(i,s) =A _(i,s) e ^(jϕ) ^(i,s)   Eq. 3

E _(i,p) =A _(i,p) e ^(jϕ) ^(i,p)   Eq. 4

where i indicates the variables' value at input.

Each interaction (indicated by a directionality arrow below withcorrelation to the paths of the light at an output node of FIG. 6B) maybe described as a 2×2 matrix multiplied by the energy of the s and pelements of Eq. 3 and Eq. 4. Such that

$\begin{matrix}{\begin{bmatrix}E_{o,{s \downarrow}} \\E_{o,{p \downarrow}}\end{bmatrix} = {{\begin{bmatrix}{\sqrt{\eta_{{s \downarrow s}arrow}}e^{j\; \varphi_{{s \downarrow s}arrow}}} & {\sqrt{\eta_{{s \downarrow p}arrow}}e^{j\; \varphi_{{s \downarrow p}arrow}}} \\{\sqrt{\eta_{{p \downarrow s}arrow}}e^{j\; \varphi_{{p \downarrow s}arrow}}} & {\sqrt{\eta_{{p \downarrow p}arrow}}e^{j\; \varphi_{{p \downarrow p}arrow}}}\end{bmatrix}\begin{bmatrix}E_{i,{sarrow}} \\E_{i,{parrow}}\end{bmatrix}} = {{OPE}_{\downarrow arrow}\begin{bmatrix}E_{i,{sarrow}} \\E_{i,{parrow}}\end{bmatrix}}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

where the left and downward are indicative of light diffracting to theleft and down, as at output node 662 of FIG. 6B, and where η is thediffraction efficiency of the transition and ϕ is the phase shift of thetransition.

Additionally, each bounce off the AR coating can be described by a 2×2matrix. In a planar coating, the off-diagonal elements of this matrixare 0, and the magnitude of the diagonal elements must be 1 due to thefact that, in a planar coating, the layers are parallel. Because thereis no diffraction from the AR coating, there are only two of thesematrices: AR_(↓↓) and AR_(←←).

$\begin{matrix}{{AR}_{\downarrow \downarrow} = \begin{bmatrix}e^{j\; \theta_{s \downarrow s \downarrow}} & 0 \\0 & e^{j\; \varphi_{p \downarrow p \downarrow}}\end{bmatrix}} & {{Eq}.\mspace{14mu} 6} \\{{AR}_{arrowarrow} = \begin{bmatrix}e^{j\; \theta_{sarrow sarrow}} & 0 \\0 & e^{j\; \theta_{parrow parrow}}\end{bmatrix}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

The electric field state leaving the output node propagating downward(towards an exit pupil expander) can now be related to the electricfield input state.

$\begin{matrix}{\begin{bmatrix}E_{o,{s \downarrow}} \\E_{o,{p \downarrow}}\end{bmatrix} = {( {{{OPE}_{\downarrow \downarrow}{AR}_{\downarrow \downarrow}{OPE}_{\downarrow arrow}{AR}_{arrowarrow}{OPE}_{arrowarrow}} + {{OPE}_{\downarrow arrow}{AR}_{arrowarrow}{OPE}_{arrow \downarrow}{AR}_{\downarrow \downarrow}{OPE}_{\downarrow arrow}}} )\begin{bmatrix}E_{i,s} \\E_{i,p}\end{bmatrix}}} & {{Eq}.\mspace{14mu} 8}\end{matrix}$

However, this may be simplified if the phase retardation (the differencebetween phase shifts of each of the s and p light paths at each bounce)is 0, such that (θ_(s)=θ_(p)). In this case, the anti-reflective coatingno longer impacts the energy output. In other words, Eq. 6 and Eq. 7 maybe replaced, respectively by:

$\begin{matrix}{{AR}_{\downarrow \downarrow} = {e^{j\; \theta_{\downarrow \downarrow}}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}} & {{Eq}.\mspace{14mu} 9} \\{{AR}_{arrowarrow} = {e^{{j\; \theta}\;arrowarrow}\begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

And the output is simplified to:

$\begin{matrix}{\begin{bmatrix}E_{o,{s \downarrow}} \\E_{o,{p \downarrow}}\end{bmatrix} = {\quad{e^{j\; \theta_{\downarrow \downarrow}} {e^{j\; \theta_{arrowarrow}}( {{{OPE}_{\downarrow \downarrow}{OPE}_{\downarrow arrow}{OPE}_{arrowarrow}} + {{OPE}_{\downarrow arrow}{OPE}_{arrow \downarrow}{OPE}_{\downarrow arrow}}} )}{\quad\begin{bmatrix}E_{i,s} \\E_{i,p}\end{bmatrix}}}}} & {{Eq}.\mspace{14mu} 11}\end{matrix}$

Therefore, if the AR coating has no phase retardation, it only imparts aphase shift to the output, with no change of polarization state ormagnitude. If the AR coating does have phase retardation, it will changethe output polarization state and magnitude, and introduce negativeoptical effects. This is critical when determining the number of layersof an anti-reflective coating used on a TIR waveguide display device.FIG. 7 depicts the phase retardation for TIR light at various angles ofincidence. FIG. 8A shows captured images of an eyepiece design for blue(455 nm) light on substrates with different n values of layers of ananti-reflective coating. FIG. 8B shows simulated images of an eyepiecedesign for blue (455 nm) light on substrates with different n values oflayers of an anti-reflective coating. FIG. 8C shows captured images aneyepiece design for red (625 nm) light on substrates with different nvalues of layers of an anti-reflective coating. FIG. 8D shows simulatedimages an eyepiece design for red (625 nm) light on substrates withdifferent n values of layers of an anti-reflective coating. Largevariation in phase difference impact the exit beams, observable as“striations” or uniformity disruptions depicted in FIGS. 8A-8D. Afour-layer anti-reflective coating is found to have the most uniformityand is thus preferred over the other coatings that are represented inFIGS. 7 and 8A-8D. It will be appreciated that the effects of adjustingthe number of anti-reflective layers are consistent across eachwavelength, that is, though FIGS. 8A-8D depict eyepieces for particularwavelengths of light the effect is similar for other wavelengths (suchas green) that are not shown.

To minimize this degradation and reduce the amount of inter-waveguidereflections while nonetheless maintaining intra-waveguide reflections,embodiments of the present invention are directed to an optimizedanti-reflective coating. Such optimization balances the index ofrefraction of the anti-reflective material with the number and thicknessof layers applied in the coating. This will minimize the phaseretardation effects by bringing θ_(s) substantially equal to θ_(p).

In some embodiments an anti-reflective coating is applied to one side ofa waveguide substrate within a waveguide stack that makes up an eyepieceof an augmented or mixed or virtual reality device. Preferably, thecoated side is on the opposing side a viewer's eye is expected to beplaced, though a coated side on a same side as a viewer's eye mayfunction similarly. In some embodiments, a grating is applied to theopposite surface of the waveguide as the coated side. Theanti-reflective coating preferably reduces reflection from and increasestransmission through the surface to which the anti-reflective coating isapplied. The anti-reflective coating preferably increases transmissionof light to at least 97 percent.

The antireflection coating comprises at least one layer, but inpreferred embodiments is less than eight and alternates layers of twoalternating constituent materials of comparatively high andcomparatively low indices of refraction. In some embodiments, one of theconstituent layers is titania (TiO₂). In some embodiments, one of theconstituent layers is silica (SiO₂).

One of skill in the art will appreciate other candidate materials, suchas SiN, ZrO₂, ZnO₂, Ta₂O₅, or NB₂O₅ or other metal oxides with lowabsorption in visible wavelength range. Such materials, as with TiO₂ andSiO₂, are well known in the art for their use in the photovoltaic orglass treatment for anti-reflection.

In some embodiments, SiO₂ is a final (i.e. top) layer of a multilayercoating as a protective layer to any wet chemistry (sulfuric acid,hydrogen peroxide, etc.) incident to waveguide cleaning, processing orpatterning.

An index of refraction, n, of a material is composed from two elements,the known refractive index and the absorption coefficient k (orimaginary index of refraction that relates to the attenuation of lightthrough the material) such that n=n+ik. Different materials havedifferent absorption coefficients that can produce widely variousresults, and this is especially variable when multiple materials arelayered together to create a net k value for the coating. For example,titania, a well know anti-reflective material, and silicon nitride SiNhave similar reflectance spectrums for normal incidence, but slightlydifferent k values. Though these may be negligible in normal/orthogonallight directions, at angles supporting TIR every bounce of the light ata surface is attenuated with a slightly different absorption as comparedbetween the two materials. The cumulative effect of this slightdifference of absorption coefficient in a coating that manipulates lightacross a plurality of bounces in a TIR system can drastically affect theoverall image quality, especially uniformity and efficiency.

Using the energy output by materials of varying absorption coefficientsk of various materials, the loss of light, as a percentage of output, isdepicted in FIGS. 9A-9D. FIG. 9A depicts the loss of energy of lightoutput by the EPE as a function of increasing layers and increasing kvalues. With an exemplary EPE efficiency of five percent as depicted,most single layer anti-reflective coatings preserve this efficiency in aTIR system, such as an optical waveguide, when the net k value is lessthan approximately 5×10⁻⁴. Each additional layer or increase in net kvalue exponentially decays the efficiency of the energy output at theEPE. This is true regardless of the material or the number of layers,though the degree of decay changes as shown by FIGS. 9B and 9C.

FIG. 9D depicts an EPE efficiency diagram demonstrating that increasedlayers, despite any benefits to anti-reflection known in the art, aredetrimental to system performance through increased loss.

In some embodiments, anti-reflective coatings with fewer than eightlayers are utilized. In some embodiments, such as an MgF₂ coating, onlya single layer is utilized.

According to Eq. 1, a target index of refraction may be resolved bysimple math, however the cumulative effect of a particular k value isnot so easily derived, and in an alternating layer coating thecumulative target n may not be so straightforward either. For example,if a conventional anti-reflective coating material like titania wereapplied to a glass substrate, Eq. 1 would not be satisfied. Glassgenerally has an index of refraction between 1.5 and 1.6, ananti-reflective coating on glass therefore should have an index ofrefraction between 1.22 and 1.27. In some embodiments of the presentinvention, an antireflection coating of MgF2 is applied (the index ofrefraction of MgF₂ is 1.38) to a glass substrate.

With reference to FIG. 3, multiple waveguides may be used, such thateach waveguide is configured to propagate a particular wavelength oflight. A distinct thickness for an anti-reflective coating for eachwaveguide may be created based on the configured wavelength of thatwaveguide. For example, in a MgF2 coating on glass configured topropagate green light (approximately 520 nm), a thickness of 94 nm isdesired. Alternatively, a common thickness for any waveguide (to save onmanufacturing application complexity) between 75 nm and 125 nm can beapplied for single layered coatings to reflect the visible spectrumgenerally, with the understanding that the exact thickness selected willbe more beneficial for the particular wavelength of light dictated byEq. 2.

Reference throughout this document to “one embodiment,” “certainembodiments,” “an embodiment,” or similar term means that a particularfeature, structure, or characteristic described in connection with theembodiment is included in at least one embodiment. Thus, the appearancesof such phrases in various places throughout this specification are notnecessarily all referring to the same embodiment. Furthermore, theparticular features, structures, or characteristics may be combined inany suitable manner on one or more embodiments without limitation.

The particulars shown herein are by way of example and for purposes ofillustrative discussion of the preferred embodiments of the presentinvention only and are presented in the cause of providing what isbelieved to be the most useful and readily understood description of theprinciples and conceptual aspects of various embodiments of theinvention. In this regard, no attempt is made to show structural detailsof the invention in more detail than is necessary for the fundamentalunderstanding of the invention, the description taken with the drawingsand/or examples making apparent to those skilled in the art how theseveral forms of the invention may be embodied in practice.

As used herein and unless otherwise indicated, the terms “a” and “an”are taken to mean “one,” “at least one” or “one or more.” Unlessotherwise required by context, singular terms used herein shall includepluralities and plural terms shall include the singular.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense as opposed to anexclusive or exhaustive sense; that is to say, in the sense of“including, but not limited to.” The term “or” as used herein is to beinterpreted as inclusive or meaning any one or any combination.Therefore, “A, B or C” means any of the following: A; B; C; A and B; Aand C; B and C; A, B and C. An exception to this definition will occuronly when a combination of elements, functions, steps or acts are insome way inherently mutually exclusive.

Words using the singular or plural number also include the plural andsingular number, respectively. Additionally, the words “herein,”“above,” and “below” and words of similar import, when used in thisdisclosure, shall refer to this disclosure as a whole and not to anyparticular portions of the disclosure.

The description of embodiments of the disclosure is not intended to beexhaustive or to limit the disclosure to the precise form disclosed.While specific embodiments and examples for the disclosure are describedherein for illustrative purposes, various equivalent modifications arepossible within the scope of the disclosure, as those skilled in therelevant art will recognize. Such modifications may include, but are notlimited to, changes in the dimensions and/or the materials shown in thedisclosed embodiments.

All of the references cited herein are incorporated by reference.Aspects of the disclosure can be modified, if necessary, to employ thesystems, functions, and concepts of the above references to provide yetfurther embodiments of the disclosure. These and other changes can bemade to the disclosure in light of the detailed description.

Specific elements of any foregoing embodiments can be combined orsubstituted for elements in other embodiments. Furthermore, whileadvantages associated with certain embodiments of the disclosure havebeen described in the context of these embodiments, other embodimentsmay also exhibit such advantages, and not all embodiments neednecessarily exhibit such advantages to fall within the scope of thedisclosure.

Therefore, it should be understood that the invention can be practicedwith modification and alteration within the spirit and scope of theappended claims. The description is not intended to be exhaustive or tolimit the invention to the precise form disclosed. It should beunderstood that the invention can be practiced with modification andalteration and that the invention be limited only by the claims and theequivalents thereof.

What is claimed is:
 1. An anti-reflective waveguide, comprising: aplanar waveguide substrate having a first index of refraction; aplurality of diffractive optical elements disposed upon a first surfaceof the waveguide; and an anti-reflective coating disposed upon a secondsurface of the waveguide.
 2. The anti-reflective waveguide of claim 1,wherein the waveguide is planar and configured to propagate light bytotal internal reflection between the plurality of diffractive opticalelements and the anti-reflective coating in a substantially firstdirection, and outcouple light in a second direction substantiallyorthogonal to the first direction.
 3. The anti-reflective waveguide ofclaim 2, wherein the light propagating by total internal reflectioncomprises an s polarization component and a p polarization component. 4.The anti-reflective waveguide of claim 3, wherein the anti-reflectivecoating is configured to reduce phase retardation between the twocomponents such that an angle of incidence of the s component issubstantially similar to that of the p component through the waveguide.5. The anti-reflective waveguide of claim 4, wherein the anti-reflectivecoating reduces reflection from and increases transmission of lightthrough the second surface into the waveguide.
 6. The anti-reflectivewaveguide of claim 5, wherein at least 97 percent of the light istransmitted through the second surface.
 7. The anti-reflective waveguideof claim 3, wherein the waveguide substrate is glass and theanti-reflective coating comprises a layer of MgF₂.
 8. Theanti-reflective waveguide of claim 7, wherein the layer of MgF₂ has athickness between 75 and 125 nm.
 9. The anti-reflective waveguide ofclaim 7, wherein the anti-reflective coating comprises a layer of SiO₂.10. The anti-reflective waveguide of claim 8, wherein the layer of MgF₂is disposed immediately adjacent to the second surface.
 11. Theanti-reflective waveguide of claim 10, wherein a layer of SiO₂ isdisposed upon the layer of MgF₂.
 12. The anti-reflective waveguide ofclaim 11, wherein a cumulative index of refraction of theanti-reflective coating has an imaginary refractive index componentvalue less than 5×10⁻⁴.
 13. The anti-reflective waveguide of claim 11,wherein a cumulative index of refraction of the anti-reflective coatinghas an imaginary refractive index component value between 5×10⁻⁴ and1×10⁻³.
 14. The anti-reflective waveguide of claim 3, wherein theanti-reflective coating is comprised less than eight layers alternatingbetween a first material and a second material.
 15. The anti-reflectivewaveguide of claim 14, wherein the anti-reflective coating consists offour layers.
 16. The anti-reflective waveguide of claim 14, wherein thefirst material has comparatively higher index of refraction than thesecond material.
 17. The anti-reflective waveguide of claim 14, whereinthe first material is TiO₂.
 18. The anti-reflective waveguide of claim14, wherein each layer of TiO₂ has an index of refraction greater than2.
 19. The anti-reflective waveguide of claim 14, wherein the secondmaterial is SiO₂.
 20. The anti-reflective waveguide of claim 19, whereineach layer of SiO₂ has an index of refraction between 1.45 and 1.58. 21.The anti-reflective waveguide of claim 20, wherein a cumulative index ofrefraction of the anti-reflective coating has an imaginary refractiveindex component value less than 5×10⁻⁴.
 22. The anti-reflectivewaveguide of claim 20, wherein a cumulative index of refraction of theanti-reflective coating has an imaginary refractive index componentvalue between 5×10⁻⁴ and 1×10⁻³.
 23. The anti-reflective waveguide ofclaim 1, wherein a cumulative index of refraction of the anti-reflectivecoating has an imaginary refractive index component value less than5×10⁻⁴.